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Model identification and selection for single-index varying-coefficient models

Author

Listed:
  • Peng Lai

    (Nanjing University of Information Science & Technology)

  • Fangjian Wang

    (Nanjing University of Information Science & Technology)

  • Tingyu Zhu

    (Oregon State University)

  • Qingzhao Zhang

    (Xiamen University)

Abstract

Single-index varying-coefficient models include many types of popular semiparametric models, i.e., single-index models, partially linear models, varying coefficient models, and so on. In this paper, a two-stage efficient variable selection procedure is proposed to select important nonparametric and parametric components and obtain estimators simultaneously. We also find that the proposed procedure can separate predictors into varying-coefficient and constant-coefficient predictors automatically. Theoretically, it has the selection and estimation consistency properties. Simulation studies and a real data application are conducted to evaluate and illustrate the proposed methods.

Suggested Citation

  • Peng Lai & Fangjian Wang & Tingyu Zhu & Qingzhao Zhang, 2021. "Model identification and selection for single-index varying-coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 457-480, June.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:3:d:10.1007_s10463-020-00757-0
    DOI: 10.1007/s10463-020-00757-0
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    References listed on IDEAS

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    3. Feng, Sanying & Xue, Liugen, 2015. "Model detection and estimation for single-index varying coefficient model," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 227-244.
    4. Huang, Zhensheng & Pang, Zhen & Zhang, Riquan, 2013. "Adaptive profile-empirical-likelihood inferences for generalized single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 70-82.
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    7. Lai, Peng & Wang, Qihua & Zhou, Xiao-Hua, 2014. "Variable selection and semiparametric efficient estimation for the heteroscedastic partially linear single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 241-256.
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